NBS

PUBLICATIONS

NBSIR 81-2337

Measurement and Evaluation

Methods for an Angular

Accelerometer

A11100 cn i4ti4^

I ini —

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Electronics and Electrical Engineering

Electrosystems Division

Washington, DC 20234

January 1 981

Final Report

Issued August 1 981

Under Department of Transportation Reimbursable Agreement

DOT-HS-0-021 93IA

c 100

. U56

81-2337

1981

c. 2

Prepared for: Department of Transportation

national Highway Traffic Safety Administration

400 Seventh St., S.W.

i/Vashington, DC 20590

NATIONAL BURBA

OF STANDARDS

UBfiABT

MEASUREMENT AND EVALUATION

METHODS FOR AN ANGULAR

ACCELEROMETER

NBSIR 81-2337

OCT 1 4 J987

/W Cull. _ &>

Qtfoo

/?o. %/-23S 7

John D. Ramboz

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Electronics and Electrical Engineering

Electrosystems Division

Washington, DC 20234

January 1 981

Final Report

Issued August 1 981

Under Department of Transportation Reimbursable Agreement

DOT-HS-9-021 93IA

Prepared for: Department of Transportation

National Highway Traffic Safety Administration

400 Seventh St., S.W.

Washington, DC 20590

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
*&£X}K — ' •
Foreword

Work described herein was performed for the National Highway

Traffic Safety Administration (NHTSA) of the Department of Transportation (DoT) under an Interagency Reimbursable Agreement

DoT-HS -9-021 93IA . The NBS Cost Center for this project was 7223403 . Laboratory efforts commenced on October 1, 1980 and were completed

on December 30, 1980. The DoT/NHTSA Technical Contract Monitor was

Mr . Mark Haffner

The tests performed and discussed in this report are abbreviated

measurements to assess the principal operating characteristics of a newly developed angular accelerometer. Time and funding constraints

required that only selected fundamental measurements could be made.

As a result of these measurements, satisfactory performance was indicated and further consideration should be given to additional

work for the development and testing of this type of transducer.

Because of the limited testing, this conclusion is preliminary.

Further testing should be done in order to reach final conclusions

as to the overall performance for the intended DoT application.

Certain commercial equipment, instruments, or materials are identified in this report in order to adequately specify the experimental procedure. In no case does such identification imply

recommendation or endorsement by the National Bureau of Standards,

nor does it imply that the material or equipment identified is

necessarily the best available for the purpose.
TABLE OF CONTENTS

Page

Foreword iii

Abstract 1

1 . INTRODUCTION 1

2. ACCELEROMETER SPECIFICATIONS AND PHYSICAL DESCRIPTION .. 2

2.1 Angular Acceleration Sensitivity 3

2 .2 Frequency Response 3

2.3 Amplitude Linearity 5

2.4 Transverse Axis Angular Sensitivity 5

2.5 Linear Acceleration Sensitivity 5

2.5.1 Linear Acceleration Sensitivity Parallel to

Sensing Axis 5

2.5.2 Linear Acceleration Sensitivity Perpendicular

to Sensing Axis 5

2.6 Physical Description 6

3. LABORATORY MEASUREMENTS 6

3.1 Resistance Measurements 7 3.2 Angular Acceleration 8

3.2.1 Test Philosophy 8

3.2.2 Electrical Excitation Power Configuration . . 8

3.2.3 Laboratory Instrumentation. Amplifiers, and

Filters 8

3.2.4 Angular Acceleration Generation 8

3.2.5 Test Measurements 12

3 .2 .5 .1 Angular Acceleration Sensitivity ... 12

3 .2 .5 .2 Amplitude Linearity Measurements ... 14

3.3 Transverse Axis Angular Sensitivity ........ 14

3.4 Linear Acceleration Testing 16

3.4.1 Test Philosophy 16

3.4.2 Linear Sensitivity Parallel to Sensitive

Axis 17

3.4.3 Linear Sensitivity Perpendicular to Sensitive

Axis 18

3 .4 .4 Other Effects 20

IV
TABLE OF CONTENTS (cont.)

Page

3.5 Measurement Uncertainties 21

3.5.1 Bridge Voltage Excitation 21

3.5.2 Signal Voltage Measurement . .21

3.5.3 Amplifier Gain and Filter Response 21

3.5.4 Acceleration Determinations 22

3.5.5 Computation and Arithmetic Errors 22

3 .5 .6 Other Error Sources 23

3.5.7 Combined Uncertainties 23

4. CONCLUSIONS 24

5. ACKNOWLEDGMENTS 25

6. REFERENCES 25

APPENDIX A A-l

APPENDIX B B-l

v

TABLE OF CONTENTS (cont.)

Page

3.5 Measurement Uncertainties 21

3.5.1 Bridge Voltage Excitation 21

3.5.2 Signal Voltage Measurement .21

3.5.3 Amplifier Gain and Filter Response 21

3.5.4 Acceleration Determinations .22

3.5.5 Computation and Arithmetic Errors 22

3 .5 .6 Other Error Sources 23

3.5.7 Combined Uncertainties 23

4. CONCLUSIONS 24

5. ACKNOWLEDGMENTS 25

6. REFERENCES 25

APPENDIX A A-l

APPENDIX B B-l

v

MEASUREMENT AND EVALUATION METHODS

FOR

AN ANGULAR ACCELEROMETER

John D. Ramboz

A transducer which measures angular acceleration

along one axis was investigated to assess three of its

performance characteristics, viz., sensitivity factor,

amplitude linearity, and response to linear (non-angular)

input accelerations. Accelerometer specifications and

response theory are presented. Test philosophy and

methodology are discussed along with measurement results.

Tests were conducted over a frequency range from 1 .5 to

100 Hz and over an acceleration range from 64 to 5000 rad/s^

Generally, the performance observed was in agreement with

the manufacturer' s preliminary specifications.

Key words: angular acceleration; angular accelerometer;

calibration; instrumentation; measurement; shock and

vibration

1 . INTRODUCTION

The Department of Transportation, National Highway Traffic

Safety Administration (DoT/NHTSA), Biomechanics Branch is studying

the mechanisms of human head impact injury and is developing injury

tolerance criteria. An understanding of these mechanisms and use of

the tolerance criteria will be of immediate benefit to automotive

occupant protection and protection headgear design. These are intended

to contribute to the established national goal of improved highway

safety

The measurement of angular head motions during impact has posed

a serious challenge to available instrumentation. To date, this

difficult measurement has not been successfully performed without

large errors and ambiguities. Measurement methods in the past have

relied on either photographic techniques or the derivation of angular

motions from linear motion measurements. Neither technique has

proven totally satisfactory and is, in any instance, very laborious.

In an attempt to establish head injury criteria, a program

which employs athletic boxers is being pursued by the DoT. Head

motions will be measured and analyzed along with qualified biomedical

1
observations. Correlation between the measured data and apparent

"injury" will lead to a threshold criteria useful in automobile

occupant safety

Transducer attachment to the boxer's head will be made by incorporating the instrumentation, including a multichannel FM transmitter,

in the orthodontic mouthpiece. Thus, with the mouthpiece tightly

gripped between the teeth, three-dimensional head motion can be

sensed and data transmitted to a ringside receiver and recorder

This approach is feasible only if a suitably small and accurate

transducer is available to sense the head motions.

A newly developed transducer [1]P which senses angular acceleration is being investigated for possible use in the "mouthpiece."

Its small size, ruggedness, and frequency response make it attractive

to consider for this application. A preliminary set of measurements

was desired to ascertain the fundamental operating characteristics

of this transducer. Based on the preliminary findings, a decision

can then be made as to whether to invest additional resources for an in-depth evaluation of such an accelerometer.

The tests performed and discussed herein are designed to determine

the angular-acceleration sensitivity factor (i.e., transfer function),

the frequency response, amplitude linearity, transverse sensitivity,

and linear acceleration sensitivity. These were felt to be the most

important of the parameters and could be assessed with hardware and

methods already available. Programmatic constraints on time and funds

necessitated a brief, but meaningful, set of tests. These are described

in this report. However, to characterize fully the transducer's

performance, additional tests would be required, but were not performed

at this time.

2. ACCELEROMETER SPECIFICATIONS AND PHYSICAL DESCRIPTION

The angular accelerometer available for testing was a developmental

prototype and, as such, may not have had all the engineering refinements

incorporated into its design. However, it was deemed worthwhile to

test it at this stage of its development in order to determine its

feasibility for use in the DoT "mouthpiece" configuration.

The manufacturer's preliminary specifications which accompanied

the accelerometer are reproduced in appendix A. The parameters of

key interest in this phase of the investigation are listed as follows:

1 Numbers in brackets refer to the references listed at the end of

this report.

2
1 . Sensitivity,

2. Frequency response,

3 . Ampl i tude 1 i neari ty

,

4. Transverse-axis angular sensitivity, and

5. Linear acceleration sensitivity.

Each of these parameters is briefly discussed and interpreted.

2.1 Angular Acceleration Sensitivity

The sensitivity factor for the transducer is the mechanical -to

electrical transfer function. As such, the transfer function is a complex ratio of the electrical output divided by the mechanical

input. The electrical output is voltage and the mechanical input is

angular acceleration in units of radians per unit time squared, or rad/s^ . The accelerometer transduction element contains an electrical

four-arm Wheatstone bridge where all four arms are active strain

sensing elements. The sensitivity factor is, therefore, a function

of the bridge excitation voltage which is specified as 10 volts dc

With the specified excitation voltage, the angular acceleration

sensitivity factor is given in appendix A as "5.7 yV« s^/rad ." Generally, it is accepted practice to give associated test conditions

for which the sensitivity applies, such as frequency and acceleration

amplitude. No such information was supplied, therefore, the value

of 5.7 yV«s2 /rad is interpreted as a nominal value. Phase

response is inferred by the resonance frequency and damping factor

and is discussed in the following section.

2 .2 Frequency Response

The frequency response specification is given as "flat (to)

within 1 dB to approximately 700 Hz." Transducers having a strain

gage type sensing element usually have "dc response" (a frequency of zero hertz), however, because of a small, pressure-equalizing, bleed

orifice in this design, the unit does not have dc response. Discussion

with the manufacturer disclosed that the response at the low end of

the spectrum is thought to roll off somewhere near 1 Hz or less [2],

Neither the manufacturer nor NBS has made measurements at this time

to assess the low-frequency roll-off.

The nonlinear response with frequency is caused by the

transducer's natural mechanical resonance which is given as about

2600 Hz. The rate of sensitivity increase as a function of frequency

below the natural resonance is controlled by the damping. The preliminary specifications state that the "phase response" is "typical of

an undamped system." With near zero damping, the response typically

increases by about 4% to 6% at 20% of the resonance frequency. In

this instance, one-fifth of the resonance is about 520 Hz.

Assuming that the transducer exhibits the typical behavior of other

types of accelerometers, i .e ., the mechanical resonant system can be

3
represented as a second-order, single-degree-of-freedom, spring-mass,

lightly damped system, the response R can be predicted by the following

relationship [3] where w is the angular stimulus frequency and wn

is the

natural mechanical resonance.

R

= /(I - w

2

/a)n

2

) 2 + (2£a)/wn ) 2

. ( 1 )

Further assuming a typical value for the fraction of critical

damping of 5 = 0.01 (i.e., mechanical Q

= 50)2, expected

response is shown in figures 1A and IB. The maximum response rise

is consistent with the assumed mechanical Q of 50 as shown by figure 1A.

Figure IB shows the same function with the frequency one decade less

than in figure 1A and also with the ordinate being greatly expanded.

The computed rise at 700 Hz is about +7.8% (or +0.65 dB) as compared

to the preliminary specification of +12% (+1 dB). It appears that

the preliminary specification is conservative or that the damping

factor may not be as assumed. The rise at 100 Hz is approximately

+0.15% and at 300 Hz is approximately +1.3%. It is anticipated that

the frequency spectrum of the angular acceleration to be measured in

the final application (i.e., boxer's head motions) will not contain

frequencies greater than several hundred hertz. This overall response

is adequate to satisfy the demands for the transient bandwidth of

the expected in measurement application.

The phase lag of the electrical output as compared to the

mechanical input is predicted by [3]

<t> = tan"'1 2£ - (w/u^)

1 - ( u/up

)

2

_

( 2 )

Again, assigning values of resonance frequency of 2600 Hz and

the fraction of critical damping of 0.01, the phase lags are 0.03°

at 100 Hz, 0.13° at 300 Hz and 0.33° at 700 Hz. These are sufficiently

small so as to be of no practical concern for the expected measurement

appl i cat ion.

^The damping factor is related to mechanical Q by the relationship

C = 1/2Q. A mechanical Q of 30 to 100 is typical of most lightly

damped accelerometer designs, therefore, Q

= 50 is a reasonable

approximation for purposes of these calculations.
2.3

Amplitude Linearity

The preliminary specifications give the amplitude linearity

specification for this angular accelerometer as "...less than 1 percent nonlinearity..." This is interpreted as: the deviation at

any amplitude from a least-squares linear-fit to the data within the

transducer's range will be less than one percent of the reading.

This is illustrated in figure 2.

2.4

Transverse Axis Angular Sensitivity

The preliminary specification for the response to transverse

angular acceleration (i.e., input angular acceleration perpendicular

to the sensing axis) is given as "3% maximum, 2% typical." This

applies for all frequencies and amplitudes throughout the transducer's

operating ranges.

2.5

Linear Acceleration Sensitivity

The response to linear input acceleration is given under two

conditions: parallel to and perpendicular to the angular sensing axis.

2.5.1 Linear Acceleration Sensitivity Parallel to

Sensing Axis

The preliminary specifications give the linear acceleration

sensitivity parallel to the sensing axis as "2.5 rad/(s^»g) from

dc to * 50 Hz, increasing directly with frequency above « 50 Hz at

about 0.05 rad/(s 2 *g*Hz). " This is shown graphically in

figure 3. This can be expressed as

2.5

rad/(s 2 *g), 0 Hz < f < 50 Hz, and

0.5 rad/(s 2 *g*Hz), f > 50 Hz .

Where plotted versus frequency, the linear sensitivity appears constant

above 50 Hz if the ordinate units are rad/(s^*g»Hz). Below a frequency

of 50 Hz, the function increases as (1/f) because the specification

contains no frequency term. This lower portion represents a constant

response of 2.5 rad/(s^*g).

2.5.2 Linear Acceleration Sensitivity Perpendicular to

Sensing Axis

The sensitivity for input linear acceleration which is perpendicular

to the angular sensing axis "increases directly with frequency (at a rate of) 0.04 to 0.05 rad/(s^*g*Hz). " This is shown in figure 3

by the dashed line below 50 Hz.

5
2.6 Physical Description

Figure 4 shows a photograph of the accelerometer. It is approximately 3 cm long with 0.5 inch hex faces to facilitate mounting.

The integral mounting post is a UNF 1/4-28 external thread. Without

the connecting cable, the accelerometer's center-of-gravity was measured on a knife edge as approximately 8.9 mm (0.35 in.) from the

base. The manufacturer gave [2] the location as about 7.6 mm

(0.30 in.) from the base. The illustration of figure 4 shows the

location for the center-of-gravity for the orthogonal planes and is

located symmetrically on the cylindrical axis of the accelerometer.

The measured mass of the accelerometer (without the electrical cable

and connector-^) was 16.5 ±0.1 grams.

The electrical connections were made through a supplied cable

having a miniature six-pin connector. The "pig-tail" leads are color

coded and were tagged with the following information:

Cable Lead Tagged Information Comment

Red

Black

White

Green

"Input +" "Input

"Output +" "Output -"

Bridge excitation

Bridge excitation

Signal output, high

Signal output, low

The principle of operation in its simplest form can be described

as a liquid filled torus having an intercepting diaphragm. As the torus

is accelerated about an axis perpendicular to the toroidal plane, a differential pressure is exerted on the diaphragm. Strain gages are mounted on the diaphragm and hence sense the differential pressure

which, in turn, is directly proportional to the angular acceleration.

3. LABORATORY MEASUREMENTS

The laboratory measurements selected for this assessment can be

divided into three sets:

A. Transducer resistance measurements,

B. Angular acceleration measurements, and

C. Linear acceleration measurements.

The resistance measurements were preliminary to all the others

to ensure that all leads and transduction elements were intact. The

angular acceleration measurements were designed to assess the most

%or mass considerations, the accelerometer is measured alone. The

connector has a mass of about 1 gram. In most applications, only

a portion of the cable dynamically loads the accelerometer as effective

mass; generally about 2 cm of cable length ( i . e . , about 0.5 gram) is

added to account for the cable's effective mass.

6
important transducer parameter, its angular sensitivity factor,

along with the frequency response and amplitude linearity. The

linear acceleration measurements were designed to evaluate the

transducer's output when rectilinear motion is applied to the angular

accelerometer. Ideally, the output should be zero under the latter

conditions and any output is interpreted as an error.

This section contains descriptions and discussions of the test

philosophy, test systems and apparatus special fixtures, test procedures,

data collection and presentation, and data analysis and discussion.

Measurement results of weight and center-of-gravity were given in

section 2.6 of this report

3.1 Resistance Measurements

The "lead-to-lead" resistance was measured for an unmounted

accelerometer to ensure that no damage had occurred in the leads,

connector, and transducer gages. A dc digital ohmmeter was used to measure the resistances. The resistance was measured with the ohmmeter

leads in a "forward" and "reversed" position to check for any possible

"polarity" effects. Table 1 gives the measurement results. The

resistance ranged from about 1200 to 1670 ohms. There was no apparent

ohmmeter-lead reversal effect; the "reversed" reading agreed with

the "forward" reading to within 0.2 ohm in the worst case. The

resistance from the shield to any other lead was an open circuit

insofar as the ohmmeter reading indicated. The resistance from the

"pig-tail" end of the shield wire and the transducer case was approximately 0.5 ohm.

The computed current drain with a 10 V dc excitation voltage

applied between the ±INPUT leads would be 5.991 mA. The measured

current with 10.000 V dc applied was 5.912 mA, or a difference from

the computed value of about -1 .3%. The accelerometer was held in a hand for several minutes and the current monitored; the "warm" current

was 5.879 mA (about 0.6% lower than the previous ambient temperature

current) . This would indicate that the overall resistance between

the ±INPUT leads was temperature sensitive and that self-heating

and external environmental heating can be expected to cause resistance

changes of perhaps several percent. The temperature coefficient of

bridge resistance was obtained from the manufacturer [4] as approximately

+0.7% per degree C (0.4% per degree F) as measured at any pair of

diametric points on the bridge.

With ±10 V dc applied between the ±INPUT leads, the dc

offset (bridge unbalance) voltage was measured as 9.22 mV under

ambient laboratory temperature conditions. This indicates that the

electrical balance of the strain gage bridge elements is rather good

(within about 0.09%). The unbalance as a function of temperature

was not measured, but should be if further testing is performed at a

1 a ter time .

7
3.2

Angular Acceleration

3.2.1 Test Philosophy

With a known angular acceleration applied to the transducer

along its sensitive axis, the accelerometer's transfer function

(i.e., sensitivity factor) can be determined by measuring its electrical

output. This simple relationship is shown below.

Sensitivity Factor = Voltage Output

Acceleration Input

The units of the sensitivity factor are volts per unit angular acceleration, or V/( rad/s2

). The preferred form of expressing these units

is V«s2 «rad“' and will be used throughout this report.

Further, the sensitivity factor is directly proportional to the

bridge excitation voltage. For all of the measurements made herein,

the bridge excitation voltage was nominally 10 V dc.

3.2.2

Electrical Excitation Power Configuration

The electrical excitation for the resistance bridge was supplied

from two separate adjustable and regulated sources. This is shown

schematically in figure 5. The two power sources were connected in

series so that the sum of the two voltages is the bridge excitation

voltage, nominally 10 V dc. The center connection of the sources is

connected to the system ground. For nominally equal bridge resistance

and no input angular acceleration, the bridge output voltage is zero. Because the four bridge arms are not all exactly equal, there is a small residual unbalance (offset) voltage. The two power supplies

were adjusted so that the sum of their two voltages always equaled

10 V dc and the two output voltages to ground were opposite and

equal. This procedure thus minimizes the dc voltages at the output

terminals of the bridge. This was necessary to avoid dc overloading

of sensitive amplifiers used in the measurement of the small ac signal outputs.

3.2.3

Laboratory Instrumentation, Amplifiers, and Filters

The electrical output from the accelerometer is a small ac voltage from a source impedance of about 1500 ohms. Even with

moderately good shielding and low noise power supplies, noise and

hum (i.e., 60 Hz related components) make accurate measurements

difficult. The nominal sensitivity given for the accelerometer was

5.7 uV«s 2 *rad“l. The test acceleration amplitudes to be used

ranged from about 64 to 5000 rad/s 2 peak. (Details of the input

acceleration are discussed in a later portion of this report.)

Multiplying the sensitivity and the angular accelerations provides

8
estimates of the voltages to be measured. For sinusoidal input

accelerations, the output voltages could be expected to range from

about 0.26 to 20.1 mV rms . To ensure adequate precision and accuracy,

the voltage measurement resolution and uncertainties should be a fraction of a percent; this requires that low-level ac signals

(at low frequencies at times) must be known to within a few microvolts.

Narrow band amplifiers were used as is shown in figure 6. The

output of the accelerometer was fed into a preamplifier/filter with

differential inputs. Low noise gains of nominally 200 or 500

were achieved in the first amplifier. Some band-pass filtering was also achieved in this preamplifier. Its output fed two cascaded

filters, each having nominally 0 dB gain (unity gain). These filters,

identified as "filter A" and "filter B" in figure 6, could be configured

as low-pass, high-pass, band-pass, or band-reject filters. The

output of filter B was connected to a digital measuring system which

measured and oscilloscopically displayed the signal .

Because the measurement system includes amplifiers and filters,

the response of the external system must be removed from the measurement to assess the transducer performance . This is shown as

Transducer Signal

Measured Signal

External Gain

Because the gain settings of each of the amplifiers and filters were

only known nominally, and further modified by the "skirt response"

of the filters, system gain had to be measured for each of the gainand filter-setting combinations used in the measurements.

3.2.4 Angular Acceleration Generation

The input angular acceleration to the accelerometer was generated

by a dual spin-axis rate-table (DSART). This device consists of two

motor-driven platforms whose rotational axes are perpendicular and

intersect. The main platform is oriented horizontally and rotates

about a vertical axis. Mounted on this horizontal platform is a second motor and platform whose axis is oriented horizontally.

Figure 7 shows a simplified drawing of the DSART platforms. Each of

the two motors is independently controllable and each of the angular

velocities is measurable. When both motors are rotating at a constant

speed, an angular acceleration is generated about the vertical axis

which is sinusoidal and predicted from

a(t) = w-|W2 sin(a)2t + 62), (3)

9
where a(t) is the angular acceleration, wi is the angular

velocity of the horizontal platform, u>

is the angular velocity

of the second platform, and t is a generalized unit of time. The

phase angle 62 is the angle between some arbitrary rotational

reference position on the upper platform and the accelerometer sensing

axis, and is generally selected such that 02 = 0 and can thus be

neglected. An accelerometer mounted on the upper platform, such

that its sensitive axis is perpendicular to the upper motor's horizontal

axis, will experience input angular acceleration as described by eq (3).

(References 5 through 7 give details of the DSART operation and theory.)

The lower main platform is servo-controlled so that its angular

velocity is constant and is selected by a set of thumbwheel switches

on the DSART 's front panel. It incorporates an optically sensed,

multi-slit disc in the velocity sensing servo-control circuit. The

velocity is selectable over a range from 0.0001 to 3200 °/s (about

1.7 urad/s to 56 ra d/s).

The upper motor is not servo-controlled and its velocity is set

manually by a multi-turn control. The velocity is sensed by a 60-tooth

circular gear and the output from the magnetic pickup is fed into an electronic counter. The counter reading is in units of revolutions

per minute (rpm) when the counter is gated at 1 second. Greater

velocity revolution can be obtained by gating the counter to 10 or

100 seconds.

As given by eq (3), the peak amplitude of the angular acceleration

is calculated by the product of the two angular velocities, w| and

o) 2

. Because the two velocities are in mixed, non-metric units,

a factor is needed to convert the product of degrees per second and

revolutions per minute to radians per second squared. (The factor

also accounts for the two factors of 2tt .

)

Hence,

where v-| is the angular velocity of the lower platform in units

of degrees per second and V2is the velocity of the upper platform

in units of revolutions per minute. For convenience, the angular

accelerations, ap^, are peak accelerations and hereafter will be

designated as a, without any subscripts.

Table 2 shows the angular velocities needed to generate the

angular accelerations at specified frequencies. Note from eq (3)

that the sinusoidal frequency of the acceleration is determined by

the velocity of the upper motor, as

(4)

10
Hz, (5) Vo

f

= —60

where V2is in units of rpm. The frequencies shown in table 2 were selected so that they are evenly spaced on a logarithmic scale.

The upper motor loses velocity stability at rates below about

100 rpm (10.5 rad/s); its maximum velocity is specified as 6000 rpm

(628 rad/s). Therefore, the maximum usable frequency range over which the DSART operates is about 1.67 to 100 Hz. The maximum angular

acceleration, because of bearing loading forces, is 7896 rad/s 2

peak4

. These limiting parameters (i.e*, v-. = 3200 °/s,

v2max

= 6000 rpm, ancl “max= ^896 rad/s^) then set the limits of

operation for the DSART. The values shown in table 2 are all within

these limits and can be derived from eqs (4) and (5).

In practice, all the frequencies and accelerations may not be

obtainable because of problems of unbalance, noise, hum pickup,

mechanical resonances, wave distortions, or motor heating. Balancing

becomes a critical and limiting factor as the test frequencies increase

(i.e., as V 2 increases). Mechanical vibration and, hence, mechanical

"noise" results from unbalanced conditions. Two-plane balancing is

required on each end of the rotating test specimen, usually with weight

increments as small as 0.5 gram.

At low velocities of the upper motor, the driving torque is very

small. Under these conditions, interactive forces between the main

platform's rotation and the upper motor's rotation cause coupled

torques to exist which can distort the desired sinusoidal motion;

that is to say that the upper motor cannot maintain a constant

angular velocity but is modulated by gyroscopically coupled torques

which exist because of the lower platform's rotation. When distorted

motions occur, the peak value of angular acceleration can no longer

be predicted simply by eq (4).

The slip rings used to conduct the signal from the rotating

platform are also a source of electrical noise. The lower rings are low-noise, mercury-wetted rings; the upper rings have simple dual

carbon brushes. The latter are orders of magnitude more noisy than

the mercury-wetted rings. The noise from the carbon brushes tends

to be in bursts of high frequency signals, the bursts being synchronized with the rotation of the upper motor. Electronic filtering is

relatively effective in minimizing the brush/ring noise.

4 The manufacturer limits the maximum operating acceleration by

specifying that the product of the two angular velocities in rpm

shall not exceed 720 000 (rpm) 2 .

11
Sixty hertz pickup hum is also a source of noise which

contaminates the acceleration-generated transducer signal. The

principal source of 60-Hz hum is from inadequate shielding and the

location of wiring within the DSART cabinet. The wiring passes

close to a power transformer within the DSART frame. Electronic

filtering can be effective in attenuating these hum components at

most frequencies of test; however, acceleration tests at 50 Hz were

not possible because the filters could not be adjusted to provide

sufficient attenuation at 60 Hz.

3.2.5 Test Measurements

3. 2. 5.1 Angular Acceleration Sensitivity

The angular accelerometer to be tested was mounted onto the

upper rotating platform of the DSART illustrated in figure 7. The

center-of-gravity of the accelerometer was located approximately 3 mm above the horizontal axis of the upper platform and was in line with

the vertical axis of the lower platform. The cable was coiled and

secured to the upper platform to prevent any whipping action. The

upper platform was balanced so that minimum unbalanced vibration

occurred over the rotational speeds from about 100 to 6000 rpm.

As shown in figure 6, cascaded filters and amplifiers were used

to minimize the noise and to increase the signal voltage to a level

suitable for digital measurement. Because the filter settings were

often close to the test frequencies, the amplifier gain response was

on the filter "skirts" and the nominal gains as indicated by the

amplifier settings were not accurate enough for these measurements.

Therefore, the cascaded gains were measured at each of the test

frequencies and the gain slope with frequency determined. In practice,

an exact frequency could not be set accurately nor maintained for more than short periods because of the speed variations and drifts of

the upper DSART motor. The velocity, V 2 , could be measured but

would differ slightly from the nominal setting. It was thus necessary

to make slight frequency corrections to the amplifier/filter gains.

Table 3 gives the nominal test frequencies, the measured gain, the

gain slope, and the filter settings.

The signal outputs from the amplifiers and filters went into a digital measuring system with averaging and data processing capabilities.

Random components of noise, jitter, and some distortions were removed

from the signal by ensemble averaging of a number of waveforms. The

number of ensembles ranged from 10 to 100, but usually numbered 25 or

50. The ensemble averaging has the effect of a low-pass filter.

After averaging the signal, it was integrated over a whole

number of sinusoidal cycles to determine and remove by calculation

any dc voltage components contributed by the amplifiers. The rms value of the waveform was determined and used as a basis for calculating

the transducer sensitivity. As shown in section 4.2.1 of this report.

12
the sensitivity is the ratio of the electrical output divided by the

mechanical input. The sensitivity factor, S, was computed by the use

of the following relationships:

{?_ 5400 E yV«s2 *rad"l, (6)

tt 2 v,v0

H [1 + 0.01 c ( f - f )]

1 2 n t n

where E is the rms voltage output from filter B, H n is the measured

gain at the nominal frequency, c is the gain slope in units of percent

per hertz and the other parameters are as previously described. The

factor of /Z is a simple conversion from rms voltage to peak voltage

for a sinusoidal waveform; this is necessary inasmuch as the acceleration

is in peak units. The frequencies, f^ and fn , are the test frequency

and the nominal frequency, respectively. The bridge excitation voltage

was maintained at 10 V dc for all the measurements.

At each test frequency and acceleration, a minimum of three

measurements were taken to compute the sensitivity factor. In some

instances considerably more than three sets of data were taken.

Figures 8 through 17 show the results graphically with the

measured sensitivity plotted versus frequency. The measured points

are represented by an asterisk (*) and the group average frequency

and average sensitivity are shown by the symbol "0." The left-hand

ordinate is the measured sensitivity plotted from 5 to 6 yV*s 2 *rad”l

the right ordinate is the percentage deviation referenced to value

of sensitivity of 5.529 yV«s 2 *rad

- '. (This value was chosen

from an early set of data at 15 Hz and at 1000 rad/s 2 because the

scatter in data is small at these operating conditions. The value

is arbitrary and has no special significance, but serves as a common

level for comparison purposes.)

The accompanying tables of appendix B for the figures B-l through

B-l 0 give the average frequency, average sensitivity, the percentage

deviation, and the number of measurements for each of the data sets

by frequency. Figure 8 is the summary of all the angular acceleration

sensitivity measurements for accelerations from 64 to 5000 rad/s2 . Overall, there are 229 measurements that are summarized in figure 8.

For example, at a frequency of 70 Hz, there are 62 data points plotted.

The average of the data as plotted in figure 8 indicates that

the transducer frequency response is relatively "flat" to within

about ±2.5% over a frequency range from 1.5 to 70 Hz. There is a general trend for the data to have an apparent increase in sensitivity

as frequency increases. The reasons for this are unknown. Theoretically,

the sensitivity rise should not be more than a small fraction of one percent at 100 Hz (see fig. IB). Without further testing, one cannot

state that the rise is a result of transducer performance, but rather

13
could be a result of systematic error in the measurement apparatus

or procedure.

3 .2 .5 .2 Amplitude Linearity Measurements

The data collected and presented in the previous section (angular

acceleration sensitivity) were regrouped and analyzed for amplitude

response. The data at each acceleration amplitude was averaged to

get a single value regardless of frequency. This is plotted and

shown by figure 9. The averaged data are shown by the plotting

symbol "1 ." The straight, sloped line is a first degree regression

fit to these data. The fit line is difficult to detect because it

is very close to the data, however, a slight difference can be seen

at 2000 rad/s 2

. Figure 10 shows the same data in terms of deviation

from the mean accelerometer sensitivity (slope of fit curve of fig. 9)

rather than accelerometer output voltage. Here, the differences

between the measured and fit values are more apparent. The maximum

difference allowable by the preliminary specification is ±1%

(see appendix A and section 2.3 of this report). Table 4 gives

tabular results in terms of the measured accelerometer sensitivity.

The column headed percentage deviation should be less than ±1% to

meet the specifications. The largest difference measured was approximately -1 .27% at 500 rad/s 2

.

It should be noted that other effects are present and "contaminate"

the data to an unknown amount. For example, there was no attempt to

separate the frequency response effect from the amplitude response

when examining the amplitude linearity. With the present data, the

frequency effect, which is included, has the tendency to make the

amplitude linearity appear worse than it would be at a single frequency.

Data from the test frequencies of 70 and 100 Hz are included in this

analysis. It was seen from the angular acceleration sensitivity

that the tests at 70 and 100 Hz tended to be of a greater-than -expected

sensitivity. It is believed that this same "data rise" at these two

frequencies may have "biased" the linear fit slightly higher than it

should be. Therefore, the value of -1 . 27% deviation at 500 rad/s 2

is probably not as significant as it would first appear. Furthermore,

other measurement uncertainties are associated with each of the

datum points shown which could easily account for the apparent "greaterthan-specification" deviation

It should also be further noted that the analysis was accomplished

and acceleration data were taken at only 10% of the transducer's

full scale of 50 000 rad/s2

; no statement can be made concerning

the response for acceleration amplitudes between the 5000 rad/s^

level to which testing was done and the full-scale range of 50 000

rad/s2.

3.3 Transverse Axis Angular Sensitivity

The sensitivity of the accelerometer to angular accelerations applied

in a direction which is transverse to the main sensing axis was not

14
performed directly. Indirect measurements of the influence of a transverse angular sensitivity on the performance are discussed below.

With the accelerometer mounted on the DSART upper platform as previously described, a component of transverse angular motion is

present by the fundamental operation of the DSART. Equation (3)

shows a phase term, 62, which, for the previous set of measurements,

was set to zero. When set to zero, the mechanical rotational reference

position is aligned in the same direction as the accelerometer sensing

axis. Under these conditions, a second component of angular acceleration

exists on the upper platform which is in quadrature, i.e., it occurs

at a mechanical rotation of 90° later. This component has the same angular acceleration, sinusoidal amplitude, w-ju^, but a phase angle

of tt/2 rads or 90°. Thus there exists, by the fundamental operation,

a quadrature motion (i.e., transverse) which is of the same amplitude

as the main, in-phase angular acceleration. So while the accelerometer

is sensing the "in-axis" angular acceleration generated by the DSART,

it is also simultaneously experiencing a transverse angular acceleration

of equal amplitude (i.e., 100% transverse input).

In theory, if the accelerometer' s phase response is accurately

measured, and the in-phase and quadrature-phase components resolved,

then the transverse sensitivity could be measured; the transverse

sensitivity would be the quadrature-phase component. This, in practice,

however, is not easy. Phase shifts in the measuring system and

transducer have to be carefully determined. For example, if the

transverse sensitivity were at a typical value of 2% of the main

angular sensitivity, the phase shift in response due to 100% transverse

input as described above calculates to be only 1 .1°. Phase shifts

due to the accelerometer resonance (see eq (2)) and, more importantly,

due to the amplifiers and filters would have to be known very precisely.

This is especially difficult when the filters are used at frequencies

near their cutoff frequencies.

A second method was considered, but the lack of time did not

allow it to be tried. If the accel erometer sensing axis were aligned

in the same direction as the rotational axis of the upper platform,

then, ideally, the angular acceleration in this direction would be zero. The accelerometer would experience 100% transverse input

motion from the main acceleration vector of the upper platform.

Again, ideally, the output measured under these conditions represents

the transverse sensitivity of the transducer. This assumes, of

course, perfect alignments of the accelerometer mounting, DSART

rotational axes, etc. It also assumes that the velocity, a>2,

of the upper platform is perfectly constant, and that no variations

in velocity occur over a one revolution. Observation has shown the

later condition is not true because of coupled gyroscopic torques

between the two rotating systems, namely, the lower and upper platforms

and their drive systems. The upper platform does not maintain a

15
constant velocity, especially at low velocities when waveform distortion

is easily observable. Velocity variations of the upper platform are indeed angular accelerations in that axis. At higher velocities,

the electric drive motor develops sufficient torque to overcome the

gyroscopic coupled torques. Also, the angular momentum is much

greater which tends to "smooth out" the variations in angular velocity.

It should be kept in mind that the angular transverse sensitivity

is a small quantity, i.e., about 2% of the main sensitivity; therefore,

signals in the order of 2/1 00 of 5 uV*s2 *rad"^ are being sought.

This alone represents a difficult measurement. Moreover, the gyroscopically coupled torques occur at the same period (or frequency)

as the transverse acceleration input vector to the accelerometer,

since both are directly related to the rotational velocity of the

upper platform. Hence one cannot easily separate the effects of

true transverse response and upper platform velocity variation (i.e.,

angular accelerations). Transverse sensitivity would better be

performed on a specially designed apparatus expressly made for the

purpose.

3.4 Linear Acceleration Testing

3.4.1 Test Philosophy

Two specifications for linear vibration sensitivity are given

by the preliminary specifications; one for input vibration parallel

to the angular accelerometer's sensing axis, and the second for

vibration perpendicular to the angular sensing axis. These specifications were discussed in section 2.5 of this report.

The ideal angular accelerometer would have zero output for

purely rectilinear input vibration. Any accelerometer output under

these conditions represents an error. Testing for these angular

accelerometer characteristics is complicated by the fact that pure

rectilinear motion does not exist on even the best of linear vibration

exciters (shakers). Cross axis motion as well as rocking modes

always are present to some finite level; the rocking modes generate

angular accelerations. Furthermore, the rocking modes change with

frequency, drive amplitude, position, direction, mass, and sometimes

temperature and time. It is, therefore, not only a difficult measurement, but one that often has little meaning unless extreme care has

been taken by very elaborately accounting for rocking modes of the

linear exciter.

The fixture to which the accelerometer was mounted was made and

mounted so that it and the accelerometer represented a moment

balanced load to the exciter, i.e., the exciter was driving its

linear acceleration vector through the effective center-of-gravity

of the fixture and accelerometer combined. The fixture was a 2.5 cm cube-shaped block of aluminum machined square so that perpendicularity

was ensured. A UNF 1/4-28 hole was tapped to accommodate the integral

16
mounting stud of the accelerometer (see fig. 4). Various UNF 10-32

threaded holes were located so that the block could be attached to

the linear exciter in a balanced manner.

The electrical and instrumentation hookups were the same as previously described for the angular acceleration tests (see section

3.2.2). The filters were set for a band-pass configuration as follows

(see fig. 6): preampl ifier/fil ter gain was 1000 and filters set to

3-Hz high pass, 10-kHz low pass; filters A and B gains were 0 dB and

filters set to 5-Hz high pass and 2-kHz low pass, respectively.

Therefore, the overall gain was nominally 1000 (+30 dB) with a band

pass of approximately 5 to 2000 Hz. Because measurements were taken

at least one octave away from each of the band limits, gain measurements

were not made as they were for the angular acceleration tests.

Furthermore, accuracy was not paramount for these linear acceleration

tests so accurate gain was not necessary.

3.4.2 Linear Sensitivity Parallel to Sensitive Axis

The accelerometer was mounted on the linear vibration exciter

so that the linear sinusoidal acceleration vector was aligned

parallel to the angular acceleration sensitivity axis. Linear accelerations were servo-controlled to a constant peak amplitude of nominally

50 m/s 2 (5 g peak). The test frequencies were manually selected

and ranged from about 25 Hz to 1000 Hz.

The linear sensitivity is referenced to the angular sensitivity

by the following relationship.

S£ = ^2E_ rad/(s 2 *g), , A*HSa (7)

where

O

S

£ is the linear acceleration sensitivity in units of rad/(s »g)

(same units as given in the preliminary specifications),

E is the rms output voltage from the amplifier and filters

(the term /7 converts the rms values to a peak value).

A^ is the linear acceleration test amplitude in units of

"g" (1 g

= 9.80665 m/s 2

),

H is the composite amplifier gain, and

Sa

is the angular acceleration sensitivity factor in units

of uV»

2 *rad"'

17
For these tests, the following parameters were set:

7

A

£ = 5 g peak (approximately 50 m/s )

,

H = 1000 (+30 dB), and

S

g

= 5.529 pV*s *rad"“ as determined from the angular

acceleration sensitivity.

Table 5 gives the measurement results over a frequency range

from about 25 to 700 Hz. A rocking mode resonance in the exciter

prevented measurements at higher frequencies. Figure 11 shows the

results graphically along with the preliminary specification which

is also plotted.

Because of the angular accelerations present in the linear

exciter's motion (rocking modes), this data may not represent the

true response of the accelerometer, but rather the combined response

of the exciter and the accelerometer. The rocking motion adds

vectorially to the linear sensitivity since the exciter's rocking or "contamination components" could either add to or subtract from the

true response. This is probably the cause of the "peak-valley"

response seen at 200 and 300 Hz in figure 11. Further, the rise in

response beyond 700 Hz is very probably due to a known rocking resonance

in the exciter near 1000 Hz. Even so, the measurement results indicate

that the linear acceleration sensitivity parallel to the angular sensing

axis is low and probably within the manufacturer's preliminary

specifications.

3.4.3 Linear Sensitivity Perpendicular to Sensitive Axis

The accelerometer was mounted on the adaptor block which was,

in turn, mounted onto the vibration exciter so that the linear

sinusoidal acceleration vector was aligned perpendicular to the

angular accelerometer's sensitive axis. As before, the linear accelerations were servo-controlled to a peak amplitude of 50 m/s^ (5 g peak).

The frequencies were manually selected and ranged from 100 to 1000 Hz.

The linear sensitivity perpendicular to the angular sensing

axis is referenced to the angular sensitivity by the following

relationship.

5' = 4^ = rad/(s 2 °g»Hz) , ^

18
where

S' is the linear acceleration sensitivity in units of

rad/(s 2# g*Hz) (same units as given in the preliminary

specifications)

,

E is the rms output voltage from the amplifiers and filters

(the factor of /2 converts the rms voltage to peak voltage),

Ao is the linear acceleration test amplitude in units of

"g" (1 g

= 9.80665 m/s 2

),

H is the composite amplifier gain,

Sa

is the angular acceleration sensitivity factor in units

of yV*s2 *rad‘l, and

f is the test frequency in Hz.

For these tests, the following parameters were selected:

O

Aj, = 5 g peak (approximately 50 m/s ),

H = 1000 (+30 dB) or as noted in table 7, and

S

a

= 5.529 pV •s^*rad”l

Equation (8) is the same as eq (7) except for the new term of

frequency, f, in the denominator.

When the angular accelerometer is mounted in the configuration

as described, the angular sensing axis is perpendicular to the linear

acceleration vector, however, rocking motions on the exciter ( i . e.

,

angular accelerations) are aligned with the angular sensing axis.

The importance of this cannot be overstated inasmuch as very small

rocking motions are directly sensed by the angular accelerometer.

In order to perform this measurement satisfactorily, one would have

to ensure that the exciter's rocking motions were indeed extremely

small. For example, at A^ = 5 g and at f = 100 Hz, the rocking

mode angular acceleration would have to be less than about 2.5 rad/s 2

in order to have negligible effect on the linear sensitivity measurement;

this is considered to be a low angular acceleration. Another way to

illustrate these small motions in a way more familiar to those working

with rectilinear vibration is to relate an equivalent angular acceleration in terms of a linear acceleration. If, as in the case above,

the angular acceleration were to be limited to 2.5 rad/s 2 at 100 Hz on

a vibration exciter having a table about 7.5 cm (3 in.) in diameter,

the maximum permissible difference in vertical linear accelerations

19
between the two edges of the table could be only about 0.00004 g peak,

small indeed, and would in itself represent a difficult measurement.

The measurements given below represent a first attempt at obtaining

some measure of linear sensitivity. Because of the above rocking

mode considerations and restraints, good quality measurements could

not be obtained. Time and funds did not permit the development of a method by which better measurements could be achieved. Table 6 gives

the measurement results over a frequency range from 100 to 700 Hz.

Figure 12 shows these results graphically.

One set of measurements was taken and evaluated by the use of

eq (8). The accelerometer's angular axis was oriented in an approximate

"cross-trunion" direction on the exciter. A second set was done by

rotating the accelerometer 90° about its angular sensitive axis and

the measurements repeated. The results of both sets of data as measured are two to four times greater than the preliminary specifications, however, it is felt that under these test conditions, the

fault likely lies with the testing exciter and method, and not with

the accelerometer. The fact that the results are this close to the

specification is regarded as a probable indication that the accelerometer's linear sensitivity is low and in the order of the preliminary

specification ( i . e . , 0.05 rad/(s^*g*Hz))

3.4.4 Other Effects

While performing the measurements for the linear sensitivity

with the acceleration perpendicular to the angular sensing axis (see

section 4.4.3), distortion was observed in the waveform. Nominally,

the waveform should have been sinusoidal, however, higher order

harmonics were present.

A swept frequency response was made over the frequency range

from about 200 to 3000 Hz and is shown in figure 13. The unfiltered

accelerometer output is plotted versus frequency. The output was

low and relatively flat at the lower end of the spectrum up to frequency

of about 1425 Hz. Several resonance rises are noted about 1425 Hz,

the most notable being at a frequency of about 2160 Hz. This resonance

was traced to the connector and top of the accelerometer case. Dwelling at this frequency, large effects could be seen on this high

Q resonance by lightly touching the connector. This resonant motion,

probably coupled through the electrical leads, caused an output from

the strain gage sensing elements.

Because this resonance is such a high Q, it can easily be excited

by subharmonically related accelerations which can have the effect

of seriously distorting the waveform. In the present accelerometer

packaging configuration, this may cause application measurement

problems. If, however, the transducer is repackaged for the DoT

application in a miniature triaxial configuration, then this case top/connector resonance would not likely exist. Any new configuration

should be tested to ensure that similar resonances do not exist.

20
3.5 Measurement Uncertainties

The uncertainties in the measurement process stem from various

sources, some of which are evaluatable, but others which are more

difficult to ascertain. A rigorous error analysis was not performed

inasmuch as to do so could consume more effort than did the measurements

themselves. The errors which are more obvious and evaluatable are discussed below and combined to obtain some reasonable measure of

uncertainty in connection to the data shown previously.

3.5.1

Bridge Voltage Excitation

The output voltage from the four-arm Wheatstone bridge within

the transducer is directly proportional to the bridge excitation

voltage and, moreover, uncertainty of the output voltage is directly

proportional to uncertainty of the excitation voltage. The voltage

was adjustable and measurable to within a resolution of ±0.02%

with an additional uncertainty of ±0.05% in the voltage magnitude.

Voltage drops in the short leads and connections were neglected.

Therefore, the total estimated uncertainty in the bridge excitation

voltage is ±0.07% worst case (direct addition) and ±0.054%

(rounded to ±0.05%) root-sum-squared (rss).

3.5.2

Signal Voltage Measurement

The amplified and filtered output voltage was measured with a digital processing oscilloscope whose digitizing resolution was 10 bits;

this translates to approximately ±0.1% of a full-scale digital

word of 1 bit in 1024 bits. The ranging sequence was in a 1-2-5

scheme where it would be possible to measure at 2/5 of full scale

before being able to down range to the next lower scale. This

effectively makes the measuring resolution 2.5 times less than at

full scale, or 2 .5 x (±0.1%) = ±0.25% of reading. It is estimated

that the integration process for dc voltage removal is accomplished

to within ±0.05%. The rms voltage integration, squaring, summing,

etc., is done to within ±0.1%. the ranging, gain, and reference

voltage is known to within ±0.1% and the readout resolution is to

five digits making its uncertainty about ±0.01%. Thus the overall

voltage measuring uncertainty is estimated to be ±0.51% worst case

and ±0.29% root-sum-squared.

3.5.3

Amplifier Gain and Filter Response

The amplifier gain was determined using a precision Kel vin-Varley

divider whose setting resolution (because of noise and drift) was about 5 parts in 2000, or ±0.25% of setting. (The uncertainties

associated with the divider ratio are in the order of a few parts

per million (ppm) and are completely overshadowed by the lack of

resolution due to system noise.)

21
The gain as a function of frequency was determined over a narrow

band (usually a few hertz) around a nominal frequency to determine

the gain slope with frequency. Referring to eq (6) (section 3 .2 .5 .1 of this report), two other terms are seen, namely, the gain slope and

frequency difference. Analysis of gain measurement data led to the

conclusion that the overall effects of gain measurement, frequency, gain

slope, noise, and drifts yielded an uncertainty of about ±0.75%

worst case and about ±0.43% root-sum-squared.

3.5.4 Acceleration Determinations

The angular acceleration generated by the DSART is principally

a function of the two angular velocities, v-j and V 2 , as shown

in eq (6). The velocity, v-j, of the lower platform has a setting

accuracy of ±0.25%, a "wow and flutter" specification of 0.1% at

1/10 of full-scale range, and a stability specification of ±0.1%.

These combine to be ±0.45% worst case and ±0.29% root-sum-squared

The velocity, V2, of the upper platform is measured by use

of a 60-tooth tachometer utilizing an electronic counter. At frequency

of 1 .5 Hz (90 rpm) , the counter resolution over a 10-second counter

gate time is ±1 part in 900, or about ±0.1%. Examination of the

data indicates that drifts and other instabilities account for approximately ±0.48% uncertainties. Combining these sources of error,

the worst case uncertainty is estimated as ±0.59% and ±0.49% for

the root-sum-squared estimated uncertainty.

The angular acceleration is the product of the two angular

velocities, therefore, the uncertainty in acceleration is approximately

the sum of the uncertainties of each of the velocities. Combining

these uncertainties leads to an estimate of the uncertainty for

angular acceleration of ±1 .04% worst case and ±0.74% root-sumsquared .

There are other sources of error in the acceleration prediction

such as nonsinusoidal waveform distortion, or rocking motions of the

DSART mechanisms which appear as angular accelerations; these effects

are not evaluated here. However, some of the influences that those sources have on the uncertainty have been included in the final

uncertainty value andareshown in section 3.5.7. In some instances,

these "other sources" of uncertainty may not necessarily be small in

comparison to those values given above. (If future work is performed

using this hardware, efforts should be made to evaluate such errors

and, if possible, reduce them.)

3.5.5 Computation and Arithmetic Errors

Calculations were performed digitally to 20-bit precision and

read to 4 decimal places. Final values are reported and discussed

to 3 decimal places, therefore, rounding errors can be interpreted

as ±1/2 part in 550 parts, or about ±0.09% of the typical sensitivity

reading.
3 .5 .6 Other Error Sources

There are a number of sources of additional errors leading to

measurement uncertainty. A few of the more elusive parameters are noise

and hum, nonsinusoidal distortion, cross-axis excitation and response,

temperature changes, DSART rocking motions, etc. These sources could represent difficult and complex error relationships which are interdependent on frequency, acceleration, temperature, and mounting

position as well as other now unknown quantities. In order to get a first order assessment of these effects, the scatter of the sensitivity

measurement results was briefly analyzed. Because it is believed

that the amplitude nonlinearities are small, the analysis was done

on a frequency-by-frequency basis. Statistically, an estimate of

the standard deviation was calculated for each set of data by frequency.

The results are shown in table 7. The estimated standard deviation

did not exceed ±3.5% for the 229 sets of data analyzed. This

value is a measure of the scatter in the measurement process as a result of some of the sources discussed previously as well as some

of the effects such as noise, distortion, cross-axis excitation,

etc., which were not assigned values of uncertainty. For this analysis,

a value of ±3.5% uncertainty is included in the error analysis to

account for the observed scatter due to unevaluatable causes.

3.5.7 Combined Uncertainties

The uncertainties discussed above are summarized below. The

"symbols" refer to the parameters as given in eq (6). The uncertainties

given are for the worst case combinations.

Symbol Source of Uncertainty ± Uncertainty %

- Bridge excitation voltage 0.07

E Measured voltage, rms 0.51

H,c, (ft

-fn ) Amplifier gain, gain slope

and frequency difference

0.75

VI, v 2 Arithmetic calculations and

round-off

0.09

a Applied angular acceleration 1 .04

- Scatter and other effects 3.5

Worst case sum Root-sum-squared

±5 .96%

±3 .76%

The worst case combination is about ±6% while

estimate is about ±4%. In examining the foregoing

in figure 18, most of the data falls within a band

the root-sum-squared

data as summarized

of ±6% except

23
perhaps the data at 100 Hz. It is felt that other causes were affecting

this data, to an extent beyond the error analysis. Overall, an estimated uncertainty of ±6% is acceptable as a realistic value in

lack of a more thorough analysis.

All of the parameters listed above except the last, “scatter and

other effects," are uncertainties which pertain to the test and

calibration equipment, and not to the performance of the accelerometer.

A portion of the accelerometer's measurement uncertainty is included

in the 3.5% value of scatter and other effects, but just how much

cannot be stated at this time. Although a value of 6% was assigned

as an estimate of overall uncertainty surrounding the entire measurement

process, it should be emphasized that the accelerometer' s contribution

is a fraction of the 6% under the conditions that these data were

obtained.

4. CONCLUSIONS

Three of the more important transducer parameters were tested

to obtain a measure of performance and to fundamentally characterize

the accelerometer. These parameters were:

(1) Angular acceleration sensitivity as a function of frequency,

(2) Angular acceleration amplitude linearity, and

(3) Linear acceleration sensitivity response.

The angular acceleration sensitivity was measured over a frequency

range from about 1.5 to 100 Hz and an acceleration amplitude range

from about 64 to 5000 rad/s2 . The mean sensitivity as described

in this report was 5.53 uV*s2 /rad at a reference frequency

of 15 Hz. Deviations of the sensitivity with frequency over a range

from 1.5 to 70 Hz was about -1.5 to +2.5% referenced to the 15-Hz mean value.

The angular acceleration amplitude linearity was measured over an acceleration range from about 64 to 5000 rad/s2 . The maximum deviation

between the measured data and a zero-based, best-fit, straight line was

about -1.27%, a moderate portion of which can be attributed to

uncertainties in making the measurement and analyzing the data.

The linear acceleration sensitivity was measured both parallel

to and perpendicular to the angular sensing axis. In the first

instance, measurements indicated performance was within the preliminary

specifications as given by the manufacturer. In the second instance,

the measurement is much more difficult and rocking motions of the

vibration exciter ( i . e .

,

angular accelerations) contaminate the data

so that good measurements could not be achieved. However, the

results were well within an order of magnitude of being within the

preliminary specifications and are small, even though a good measure

could not be done.

24
Overall, based on the limited measurement results obtained and

from the observed performance, it is felt that the quality is probably

adequate for the current DoT application of measuring angular head

motions. However, the accelerometer packaging configuration must be

changed and adapted to the DoT application which would then require

additional testing to ensure that the transducer performance was maintained.

Future testing should be done at a greater depth ( i . e. , more

thoroughly), other parameters tested, and an attempt made to reduce

the overall measurement uncertainties.

5. ACKNOWLEDGMENTS

Appreciation is given to Mark Haffner, the DoT/NHTSA technical

contract monitor, for his support and guidance concerning the ultimate

application for the type accelerometer and also for his probing

questions regarding transducer operation and testing methodology.

Thanks are extended to Bob Sill of Endevco regarding details of the

accelerometer design and construction as well as interpretation of some of the specifications. Thanks also to several NBS co-workers

who contributed suggestions.

6. REFERENCES

[1] Endevco angular accelerometer, model 7302, serial no. 102

prototype.

[2] Personal communication with R. Sill of Endevco, October 14, 1980.

[3] Harris, C. M., Crede, C. E., "Shock and Vibration Handbook,"

Second Edition, McGraw-Hill, New York, 1976, p. 2-9.

[4] Personal communication with R. Sill of Endevco, November 17, 1980.

[5] Ramboz, J. D., Angular Acceleration Generation Using a Dual

Spin-Axis Rate-Table. Nat. Bur. Stand. (U.S.) NBSIR 81-xxxx,

being prepared.

[6] McCuskey, S. W., "Introduction to Advanced Dynamics," AddisonWesley, Reading, Mass., 1959, pp. 120-124.

[7] "Handbook of Instructions, 1100 series. Rate Tables," Genisco

Technology Corporation, Compton, Calif., June 1, 1973.

25
Table 1 - Transducer gage resistance measurements;

values are in units of kilohms.

Red meter lead

+INPUT -INPUT +0UTPUT -OUTPUT SHIELD

Black

meter

lead

+INPUT -- 1.66 1.32 1.27 00

-INPUT 1.67 — 1.26 1.21 00

+0UTPUT 1.32 1.26 -- 1.66 00

-OUTPUT 1.27 1.21 1.66 -- 00

SHIELD 00 00 00 00 --

26
Table 2-

Angular

velocities

v,

and

v~

for

calculated

peak

acceleration,

7896 11 11 11 01 11 ! 00<3- 00

1440 1029 720 0 00 cu 00 1 1 1 | 0 0 CO r— CO 0 1 l 1 § 0 0 r— cu 03 ID

r-'. CO

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rpm x

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rad/s
Table 3 - Measured gains and gain slope corrections for the cascaded

filters and amplifiers used for the angular acceleration sensitivity

measurements. (LP = low pass, HP = high pass)

Nominal

^Frequency

Hz

l 1.5

2

3

j 3

5

I

) 15

j 15

i 15

1 15

30

30

70

70

70

100

11

i

l P.ain

Filter Settings \

Nominal

Gain

Measured

Gain

\ Slope

I %/Hz

Preamp.

Hz

| Filter A

Hz

! Filter B Hz

500 500.00 1 0.00 .03HP/30LP | 1 5LP 15LP

500 413.87 j -1.64 .03HP/3LP 4LP j 4LP

| 500 498.75 -0.201 .03HP/30LP 1 5LP 15LP

200 199.32 -0.401 .03HP/30LP 15LP 15LP

500 493.91 -0.640 .03HP/30P 15LP 1 5LP

500 484.49 -1.064 .03HP/30LP 1 5LP 15LP

500 498.50 -0.149 .03HP/100LP 30LP 30LP

500 491.88 -0.439 .03HP/100LP 30LP 30LP

500 479.24 +0.144 3HP/100LP 30LP 30LP

200 196.62 -0.432 .03HP/100LP 30LP 30LP

200 190.49 +0.467 3HP/100LP 30LP 30LP

500 474.84 -0.496 3HP/100LP 55LP 55LP

200 188.14 -0.545 3HP/100LP 55LP 55LP

500 379.35 +2.714 3HP/300LP 60HP 60HP

500 428.63 +2.056 3HP/300LP 60HP 150LP

200 171.17 +2.89 3HP/300LP 60HP 150LP

500 449.68 -0.698 3HP/300LP 65HP 150LP

28
Table 4 - Amplitude linearity data over 10 percent of the

acceleration full-scale range of 50 000 rad/s^.

Reference sensitivity was 5.53 yV*s 2 /rad;

% deviation is deviation between fit

value and measured value

Acceleration

rad/s^

Meas. Sensitivity

yV • s 2 /rad % Deviation

64 5.486 -0.80

100 5.472 -1.05

250 5.503 -0.49

500 5.46 -1.27

1000 5.531 +0.02

2000 5.498 -0.58

3000 5.567 +0.67

4000 5.575 +0.81

5000 5.573 +0.78

29
Table 5 - Linear acceleration sensitivity

parallel to the angular acceleration

sensitive axis

Frequency

Hz

| Linear Sensitivity

rad/s2»g

Preliminary Spec.

rad/s2.g

24.5 | 0.66 ! 2.5

50 0.80 2.5

100 2.10 5.0

S 150 4.2 7.5

;

ro oo 8.4 10.0 1

j

| 250 3.0 12.5

8 300 12.6 15.0

j 350 17.5 17.5

400 22. 8* 20.0

500 29.

a 25.0

600 37.

a 30.0

700

» 45.

a 35.0

a This value contains angular acceleration components

due to the rocking motion of the vibrator exciter

and is therefore greater than the "pure linear response."

The exact amount is unknown, but shown to indicate a trend in the linear acceleration response with frequency.

30
Table 6 - Linear acceleration sensitivity perpendicular

to the angular acceleration sensitive axis for

two positions; see text for explanation

Frequency

Hz

Linear Sensi tivityc

, rad/s2«g*Hz

Position 1 Position 2

100 0.180 0.089

150 0.112 0.055

200 0.121 0.059

250 0.109 0.054

300 0.180 0.090

350 0.199 0.100

400 0.204 0.102

500 0.149 0.075

600 0.186b —

700 0. 277a >b

a Gain, H, was set to 500 rather than 1000.

^Harmonic distortion present in waveform.

c Values shown also have a vector component included

due to rocking motion (i.e., exciter angular

acceleration) causing values to be larger than the

true linear response.

31
Table 7 - Results of the analysis for an estimate of standard deviation calculated

from 229 data sets. See figure 18 for

a plot of the data

Freq. , Hz No. of Meas.

Estimated

% Std. Dev.

j

1 9 1 • 1 I 3 9 1.5

5 15 1.0 i 7 18 3.3 |

| 10 21 3.2

15 42 1.3

30 29

5 1.0

70 62 3.2

100

l 24 3.1

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SPECIFICATION

***

35

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amplitude

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preliminary

specification.
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Hz
37

angular

accelerometer.
NOTE

POWER SUPPLIES AJUSTED TO NOMINALLY 5 VOLTS EACH.

Figure 5. Transducer bridge elements and split power supplies to

force output residual voltage to near zero volts.

38
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Accelerometer,

amplifiers.
40

Figure

7.

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measurement

data

results

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the

amplitude

linearity;

accelerometer

output

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acceleration

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Figure

12.

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measurement

results

perpendicular

to

the

angular

sensitivity

axis.

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shown

for

two

orientations

of

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accel

erome

ter

about

its

sensing

axis.

Results

are

approximate

and

are

"contaminated"

with

rocking

motion

of

the

exciter.
Figure 13. Resonant response of the acce 1 e romete r when excited

by linear acceleration pe rpendi cul ar to the angular sensing

axis.

47

APPENDIX A

Preliminary Specification

7302 Angular Accelerometer S/N 102

Sensitivity

Full Scale

Frequency Response

Phase Response

Mounted Resonant Frequency

Linear Acceleration Sensitivity

Parallel to mounting surface:

Parallel to transducer axis:

5.7 yV-sec 2 /radian with 10 V

excitation

50 000 rad/sec 2

Flat within 1 dB to approximately 700 Hz

Typical of undamped system

2600 Hz

Increases directly with frequency

rad

0.04 to 0.05

sec 2 - G - Hz

2.5 rad/sec 2 - G from dc to«50 Hz,

increasing directly with frequency

above « 50 Hz at about 0.05 rad/sec 2 - G - Hz

Transverse Axis Angular Sensitivity 3% maximum, 2 % typical

Shock Limits

Angular

Linear

Amplitude Linearity

« 500,000 rad/sec 2

« 5000 G's

Less than 1% nonl i neari-ty

Temperature +10% at 25°F

-15% at 1 75°F

Physical Description

Electrical Connection

Maximum Mounting Torque

15 grams, 3 cm long, stainless steel case with 1/2" hex faces, 1/4 x 28

mounting post

Six-pin receptacle

One foot-pound

A-l

APPENDIX B

FREQUENCY RESPONSE MEASUREMENT DATA

B-l
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09-DEC-80

09:37:20

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Figure

B-3B.

Angular

acceleration

measurement

results*

frequency

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an

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of

250

rad/s 2
09-OEC-80

10.24:20

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Figure

B-4A.

Angular

acceleration

measurement

results;

sensitivity

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at

an

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of

500

rad/s

2

.
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B-9
09-DEC-80

10:27:18

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Figure

B-5A.

Angular

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measurement

results;

sensitivity

vs

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at

an

acceleration

of

1000

rad/s*.
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09-DEC-80

10,31.07

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Figure

B-6A.

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Figure

B-6B.

Angular

acceleration

measurement

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sensitivity

vs.

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an

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of

2000

rad/s 2.
08-DEC-80

09:

14:56

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Figure

B-7A.

Angular

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measurement

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sensitivity

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an

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of

2500

rad/s^.
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Figure

B-7B.

Angular

acceleration

measurement

results;

sensitivity

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an

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of

2500

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09-DEO80

10,35.11

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B-8A.

Angular

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an

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3000

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B-9A.

Angular

acceleration

measurement

results;

sensitivity

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at

an

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of

4000

rad/s*.
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X

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B-9B.

Angular

acceleration

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sensitivity

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at

an

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U.S. DEPT. OF COMM.

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BIBLIOGRAPHIC DATA

SHEET (See instructions) TITLE AND SUBTITLE

PUBLICATION OR 2 REPORT NO.

. Performing Organ. Report No. 3. NBSIR 81-2337

Publication Date August 1981

Measurement and Evaluation Methods for an Angular Accelerometer

5. AUTHOR(S)

John D. Ramboz

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions) 7. Contract/Grant No. NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

8

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City, State, ZIP)

D0T-HS-9-021 93IA

. Type of Report & Period Covered

Final Report

8/1/80 - 12/30/80

Department of Trans porta ti on

National Highway Traffic Safety Administration

400 Seventh St . , S . W

Washington, D.C. 20590

10. SUPPLEMENTARY NOTES

~| Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

A transducer which measures angular acceleration

along one axis was investigated to assess three of its

performance characteristics, viz., sensitivity factor,

amplitude linearity, and response to linear ( non-angul ar

)

input accelerations. Accelerometer specifications and

response theory are presented. Test philosophy and

methodology are discussed along with measurement results.

Tests were conducted over a frequency range from 1.5 to

100 Hz and an acceleration range from 64 to 5000 rad/s^.

Generally, the performance observed was in agreement with

the manufacturer's preliminary specifications.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

Angular acceleration; angular accelerometer; calibration;

instrumentation; measurement; shock and vibration.

13. AVAILABILITY 14. NO. OF

PRINTED PAGES

(_}(J Unlimited

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15. Price 20402.

[325 Order From National Technical Information Service (NTIS), Springfield, VA. 22161 $9.50

USCOMM-DC 6043-P80